Hexagonal multiple phase-and-amplitude-shift-keyed signal sets

Selection of a particular signal set array for a bandwidth-constrained multiple phase-and-amplitude-shift-keyed (MPASK) communication system for a linear additive Gaussian noise channel requires consideration of factors such as average and/or peak power vs symbol error probability, signal amplitude dynamic range, simplicity of generation and detection, and number of bit errors per symbol error (Gray code properties). A simple technique is presented for generating and optimally detecting the honeycomb (hexagonal) signal set, i.e., the signal set that has the tightest sphere-packing properties. The symbol and bit error probability performance of this set is compared to other two-dimensional signal sets that have been investigated in the literature, and is shown to be slightly superior from an average power standpoint. The paper concludes with a comparison of all of these signal sets from the standpoint of the factors listed above.